1. Field of the Invention
This invention relates to the field of digital communications, and in particular to a method and apparatus for tracking the phase of a received linearly-modulated signal.
2. Description of Related Art
In a typical digital communications system, digital modulation techniques, such as phase modulation techniques, are used to transmit data using an analog waveform. This waveform is typically an RF carrier, but such techniques are also used in wireline systems.
The data is usually modulated onto the carrier using a digital phase modulation. A simple form of digital phase modulation is phase-shift keying (PSK). This involves changing the phase of the transmitted waveform. These finite phase changes represent digital data. In its simplest form, a phase-modulated waveform can be generated by using the digital data to switch between two signals of equal frequency but opposing phase. If the resultant waveform is multiplied by a sine wave of equal frequency, two components are generated: one cosine waveform of double the received frequency and one frequency-independent term whose amplitude is proportional to the cosine of the phase shift. Filtering out the higher-frequency term yields the original modulating data prior to transmission.
Quadrature phase-Shift Keying (QPSK) takes the concept of PSK a stage further. The number of phase shifts is not limited to only two states. With QPSK, the carrier undergoes four changes in phase and can thus represent a group of 2 binary bits of data, known as a symbol. The phase shift on a carrier can be demodulated into a varying output voltage by multiplying the carrier with a sine-wave local oscillator and filtering out the high-frequency term. Unfortunately, the phase shift is limited to two quadrants; a phase shift of π/2 cannot be distinguished from a phase shift of −π/2. Therefore, to accurately decode phase shifts present in all four quadrants, the input signal needs to be multiplied by both sinusoidal and cosinusoidal waveforms, the high frequency filtered out, and the data reconstructed. In Offset Quadraphase Phase Shift Keying (OQPSK), the I or P components of the signal are delayed by half a symbol period.
Forward error correcting (FEC) techniques are used to include redundancy in the transmitted data, and this redundancy enables the original data to be recovered at the receiver in the event of noise, typically at low signal-to-noise ratios. There is a trade-off between the amount of redundancy included in the transmitted signal and the transmission rate or signal-to-noise ratio.
Modern parallel-concatenated (turbo codes) used for forward error correction allow for efficient operation at very low signal-to-noise ratios. A turbo encoder consists of a combination of two simple encoders. The input is a block of k information bits. The two encoders generate parity symbols from two simple recursive convolutional codes, each with a small number of states. An interleaver permutes the original k information bits before input to the second encoder. The permutation P allows that input sequences for which one encoder produces low-weight codewords will cause the other encoder to produce high-weight codewords. Thus, even though the constituent codes are individually weak, the combination is very powerful.
Wireless and passband wireline digital communications receivers typically incorporate timing, frequency and phase tracking functions which are followed by forward error correction (FEC) decoding in order to recover the original data. These functions are accomplished using digital signal processing techniques in most current receivers.
At the receiver, timing, frequency and phase estimation tasks must be performed in order to recover the original data. These tasks may be carried out either serially or jointly, with simultaneous estimation of multiple parameters. A number of phase tracking techniques have been developed for linearly modulated passband communications. See, for example, Mengali, U. and D'Andrea, A. N., Synchronization Techniques for Digital Receivers, Plenum Press, New York, 1997; and Meyr, H., Moeneclaey, M., Fechtel, S. A, Digital Communications Receivers: Synchronization, Channel Estimation, and Signal Processing, John Wiley & Sons, Inc., New York, 1998, the contents of which are herein incorporated by reference. These techniques can generally be divided into two classes: feedback and feedforward phase estimators.
A feedback phase estimator typically performs per-symbol processing in an iterative manner: for each symbol, the previous symbol phase estimate is used to extract a phase error value, which is then low-pass filtered. The low-pass filter output is used to update the previous symbol phase estimate. For phase recovery of linearly modulated signals, the phase error recovery process is designed to minimize the effect of signal modulation on the phase error estimate. Two common approaches are the use of decision-directed or maximum likelihood phase error detectors.
Feedforward phase estimators perform modulation-dependent mathematical operations on the symbols to remove the effect of modulation without the use of a current phase estimate. The output quantities of this process are smoothed, following which a feedback phase unwrapping operation is performed (if required). Finally, the phase estimates are extracted from the smoothed, unwrapped quantities. For example, with quadrature phase shift keying (QPSK) modulated signals, the complex baseband symbols can be raised to the fourth power to remove the effect of modulation. The fourth-power quantities are smoothed and phase-angle is extracted, following which a phase unwrapping process is applied. The phase estimates can then be formed as ¼ of the unwrapped phase angles.
The error rate performance of a typical digital communications system is usually constrained by the performance of the forward error correction code; other demodulator functions such as phase tracking/estimation introduce relatively small losses from the error rate which can be provided by the FEC code at a given signal-to-noise ratio (SNR) on an additive white Gaussian noise channel.
Advances in forward error correction coding such as parallel-concatenated (turbo) and serial-concatenated convolutional codes and low density parity check codes, along with iterative decoding techniques, have enabled communications with greater power efficiency than previously attainable. With the lowered minimum operating SNR this implies, the phase tracking component of the demodulator must also be capable of improved performance. Otherwise, the phase tracker can become the limiting factor for the link error rate performance, and the benefit of the FEC codes' improved performance cannot be achieved.